Related papers: On the k-pairs problem
We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of the network where messages combine and coding occurs. We give…
Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected…
We consider the following problem: Given an undirected (mixed) network and a set of ordered source-target, or cause-effect pairs, direct all edges so as to maximize the number of pairs that admit a directed source-target path. This is…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
The problem of maximum rate achievable with analog network coding for a unicast communication over a layered wireless relay network with directed links is considered. A relay node performing analog network coding scales and forwards the…
Non-adaptive joint source network coding of correlated sources is discussed in this paper. By studying the information flow in the network, we propose quantized network coding as an alternative for packet forwarding. This technique has both…
We consider the problem of computing the capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on mixed integer programming. As an application of our approach, we recover, extend…
We apply a Bethe-Peierls approach to statistical-mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices. Using the NP-hard optimization problem of…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
In the All-Reduce problem, each one of the K nodes holds an input and wishes to compute the sum of all K inputs through a communication network where each pair of nodes is connected by a parallel link with arbitrary bandwidth. The…
Let m and r be two integers. Let G be a connected r-regular graph of order n and k an integer depending on m and r. For even kn, we find a best upper bound (in terms of r and m) on the third largest eigenvalue that is sufficient to…
The Erd\H{o}s-S\'os conjecture states that the maximum number of edges in an $n$-vertex graph without a given $k$-vertex tree is at most $\frac {n(k-2)}{2}$. Despite significant interest, the conjecture remains unsolved. Recently, Caro,…
We study a new connection between a technical measure called $\mu$-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters…
Networks are a general language for representing relational information among objects. An effective way to model, reason about, and summarize networks, is to discover sets of nodes with common connectivity patterns. Such sets are commonly…
Systems with two types of agents with a preference for heterophilous interaction produces networks that are more or less close to bipartite. We propose two measures quantifying the notion of bipartivity. The two measures--one well-known and…
Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…
We study the problem of finding the smallest set of nodes in a network whose removal results in an empty $k$-core; where the $k$-core is the sub-network obtained after the iterative removal of all nodes of degree smaller than $k$. This…
We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…
The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and ask for the optimal value of one of them while…
We improve the best known lower bounds on the exponential behavior of the maximum of the number of connected sets, $N(G)$, and dominating connected sets, $N_{dom}(G)$, for regular graphs. These lower bounds are improved by constructing a…